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 A286480 Compound filter (prime signature of n & prime signature of n+d(n)): a(n) = P(A046523(n), A286479(n)), where P(n,k) is sequence A000027 used as a pairing function and d(n) is number of divisors of n (A000005). 3
 2, 12, 5, 14, 5, 61, 12, 179, 109, 61, 5, 265, 23, 142, 27, 226, 5, 607, 23, 148, 42, 61, 12, 1509, 109, 601, 44, 148, 5, 625, 23, 698, 27, 61, 61, 1117, 23, 601, 27, 2509, 5, 850, 80, 265, 148, 142, 12, 1426, 109, 607, 61, 148, 23, 430, 27, 3765, 27, 61, 5, 8575, 80, 601, 148, 2144, 61, 625, 23, 148, 27, 1741, 5, 8587, 80, 601, 363, 148, 216, 625, 138, 5719 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Pairing Function FORMULA a(n) = (1/2)*(2 + ((A046523(n)+A286479(n))^2) - A046523(n) - 3*A286479(n)). MATHEMATICA f[n_] := If[n == 1, 1, Times @@ MapIndexed[Prime[First[#2]]^#1 &, Sort[FactorInteger[n][[All, -1]], Greater]]]; Table[(2 + (#1 + #2)^2 - #1 - 3 #2)/2 & @@ {f@ n, f[n + DivisorSigma[0, n]]}, {n, 80}] (* Michael De Vlieger, May 21 2017 *) PROG (PARI) A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from Charles R Greathouse IV, Aug 17 2011 A286479(n) = A046523(n+numdiv(n)); A286480(n) = (1/2)*(2 + ((A046523(n)+A286479(n))^2) - A046523(n) - 3*A286479(n)); (Scheme) (define (A286480 n) (* (/ 1 2) (+ (expt (+ (A046523 n) (A286479 n)) 2) (- (A046523 n)) (- (* 3 (A286479 n))) 2))) (Python) from sympy import factorint, divisor_count def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2 def P(n):     f = factorint(n)     return sorted([f[i] for i in f]) def a046523(n):     x=1     while True:         if P(n) == P(x): return x         else: x+=1 def a286479(n): return a046523(n + divisor_count(n)) def a(n): return T(a046523(n), a286479(n)) # Indranil Ghosh, May 21 2017 CROSSREFS Cf. A000005, A046523, A282231, A286479, A286530. Sequence in context: A333544 A005760 A155892 * A286256 A239111 A112100 Adjacent sequences:  A286477 A286478 A286479 * A286481 A286482 A286483 KEYWORD nonn AUTHOR Antti Karttunen, May 21 2017 STATUS approved

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Last modified January 18 11:57 EST 2022. Contains 350455 sequences. (Running on oeis4.)